How does this data get populated and what would you want your end result to look like?
If you're keying in data manually it seems fairly simple to add the old name into the "Synonyms" text field you have, and update the "Taxon Name" field with the new name, and so this leads me to believe that there's something about the way the data gets populated or you have a specific idea of what you'd like it to look like when it's done?
I would create a new table called "Synonyms" in which the primary key is the synonym, and add a column of "Link to another record" type that links it back to the original plant that it came from.
This table will allow you to see all synonyms together, and you should be able to see all synonyms associated with a specific from the "Taxa" table.
hope this helps 🙂 are you looking to do these steps as an automation?